On $k$-to-1 transformations

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Involutions on a group of Möbius transformations 1 Möbius transformations

certain restrictions on the entries of A such that ψ(x) = (ax+ b)(cx+ d)−1, x ∈ Rn, and cx+ d 6= 0. Let O(n) be the real orthogonal group, i.e., the group of invertible linear transformations of Rn that preserve the inner-product K. For any v ∈ Rn, let v⊥ = {x ∈ Rn : K(x, v) = 0}, span(v) = {αv : α ∈ R}, and let ‖v‖ = K(v, v)1/2 be the Euclidean norm. Suppose v is a unit vector, i.e., ‖v‖ = 1. ...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

On the family of Diophantine triples { k − 1 , k + 1 , 16 k 3 − 4 k }

It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.

Languages of k-interval exchange transformations

This paper gives a complete characterization of those sequences of subword complexity (k− 1)n + 1 that are natural codings of orbits of k-interval exchange transformations, thereby answering an old question of Rauzy.